Analysis and Simulation of Discrete, Spatially-extended Dynamical Systems

Research - Groups/Strengths

• Statistical Analysis and Computation Methods and Stochastic Models
• Symmetry/Integrability Analysis and Computer Algebra for Nonlinear Differential Equations
• Computational Methods for Variational Problems
• Analysis and Simulation of Discrete, Spatially-extended Dynamical Systems
• Computational Algebra and Number Theory
• Computer Algebra Algorithms and Parallel Computing
• Computational Topics in General Relativity, Gauge Theory, Classical Mechanics

Analysis and Simulation of Discrete, Spatially-extended Dynamical Systems

H. Fukś has expertise in theory and applications of fully discrete dynamical systems such as cellular automata (CA) and lattice gas automata (LGA), with emphasis on dynamics of localized structures, role of invariants, and practical applications of spatially-extended discrete dynamical systems in modeling of physical and biological phenomena.

Representative publications

1. H. Fukś, 
2. “Second order additive invariants in elementary cellular automata”, arXiv:nlin.CG/0502037. Fundamenta Informaticae 75 (2006) 1-14
3. H. Fukś, “Dynamics of CA rule 142”, Complex Systems, 16:123- 138 (2005)
4. H. Fukś, A. Lawniczak, and R. Duchesne, “Effects of population mixing on the spread of SIR epidemics”, Eur. Phys. J. B, 50, 209-214 (2006)
5. H. Fukś, “Critical behaviour of number-conserving cellular automata with nonlinear fundamental diagrams”, J. Stat. Mech.: Theor. Exp. (2004) P07005
6. H. Fukś, “Probabilistic cellular automata with conserved quantities”, Nonlinearity 17:159- 173 (2004)
7. 3. H. Fukś (with N. Boccara), "Number-conserving cellular automata" Fundamenta Informaticae 52, 1-13 (2002)
8. 4. H. Fukś (with A. Lawniczak, S. Volkov), "Packet delay in data network models" ACM Transactions on Modeling and Computer Simulation 11, 233 - 250 (2001)